Clustering Quality Measures Research Articles

Cognitive reserve, depressive symptoms, obesity, and change in employment status predict mental processing speed and executive function after COVID-19.

The risk factors for post-COVID-19 cognitive impairment have been poorly described. This study aimed to identify the sociodemographic, clinical, and lifestyle characteristics that characterize a group of post-COVID-19 condition (PCC) participants with neuropsychological impairment. The study sample included 426 participants with PCC who underwent a neurobehavioral evaluation. We selected seven mental speed processing and executive function variables to obtain a data-driven partition. Clustering algorithms were applied, including K-means, bisecting K-means, and Gaussian mixture models. Different machine learning algorithms were then used to obtain a classifier able to separate the two clusters according to the demographic, clinical, emotional, and lifestyle variables, including logistic regression with least absolute shrinkage and selection operator (LASSO) (L1) and Ridge (L2) regularization, support vector machines (linear/quadratic/radial basis function kernels), and decision tree ensembles (random forest/gradient boosting trees). All clustering quality measures were in agreement in detecting only two clusters in the data based solely on cognitive performance. A model with four variables (cognitive reserve, depressive symptoms, obesity, and change in work situation) obtained with logistic regression with LASSO regularization was able to classify between good and poor cognitive performers with an accuracy and a weighted averaged precision of 72%, a recall of 73%, and an area under the curve of 0.72. PCC individuals with a lower cognitive reserve, more depressive symptoms, obesity, and a change in employment status were at greater risk for poor performance on tasks requiring mentalprocessing speedand executive function. Study registration: www.ClinicalTrials.gov , identifier NCT05307575.

Novel building energy performance-based climate zoning enhanced with spatial constraint

Existing buildings' climate zoning approaches often overlook the incorporation of building energy usage data, leading to discrepancies between climate zoning classifications and the ever-increasing demands for energy efficiency in modern construction practices. This research proposes a novel spatially constrained approach that incorporates multivariate clustering and building energy needs indicators to create a climate classification aligned with buildings' energy performance patterns. The study focuses on Kazakhstan as a case study, where buildings experience distinct climatic conditions across different regions. A spatial constraint was used to enhance hierarchical and k-means clustering methods, which were applied to the space heating and cooling energy needs of the most typical building archetypes. The quality of clustering results was evaluated using uniqueness and dispersion indicators. Furthermore, The Adjusted Rand Index was introduced to compare the proposed method with the ASHRAE and the official buildings' climate map of Kazakhstan. The existing climate maps failed to match the patterns of building energy performance. Overall, the proposed spatially constrained method exhibits promising results and offers optimized buildings' climate zoning supported by buildings' energy performance data and rigorous measures of clustering quality.

Medoid Silhouette clustering with automatic cluster number selection

The evaluation of clustering results is difficult, highly dependent on the evaluated data set and the perspective of the beholder. There are many different clustering quality measures, which try to provide a general measure to validate clustering results. A very popular measure is the Silhouette. We discuss the efficient medoid-based variant of the Silhouette, perform a theoretical analysis of its properties, provide two fast versions for the direct optimization, and discuss the use to choose the optimal number of clusters. We combine ideas from the original Silhouette with the well-known PAM algorithm and its latest improvements FasterPAM. One of the versions guarantees equal results to the original variant and provides a run speedup of O(k2). In experiments on real data with 30000 samples and k= 100, we observed a 10464× speedup compared to the original PAMMEDSIL algorithm. Additionally, we provide a variant to choose the optimal number of clusters directly.

Recent methods on short text stream clustering: A survey study

AbstractThe volume and the velocity of data in social media are increasing and the social media has become a very useful environment to detect and track the real‐world events. However, to fulfill this, it is crucial to group‐related texts according to their topics and clustering takes an essential role at this point since we have no prior knowledge about the topics and their evolution in social media. In this survey, we review the current approaches and techniques proposed for short text stream clustering in recent years. The reviewed techniques are grouped according to their methodology and discussed in detail. Also, the datasets utilized to evaluate the performance of the proposed methods and the results are summarized together with the clustering quality measures used for these evaluations. Furthermore, current challenges about short‐text stream clustering are discussed.This article is categorized under: Data: Types and Structure > Streaming Data

Study on Intelligent Analysis and Processing Technology of Computer Big Data Based on Clustering Algorithm

Aim: Clustering belongs to unsupervised learning, which divides the data objects into the data set into multiple clusters or classes, so that the objects in the same cluster have high similarity Background: The clustering of spatial data objects can be solved by optimization based on the clustering objective function. Objective: Study on intelligent analysis and processing technology of computer big data based on clustering algorithm. Methods: First, a new dynamic self-organizing feature mapping model is proposed, and the training algorithm of the model is given. Then, the spectral clustering technology and related concepts are introduced. The spectral clustering algorithm is studied and analyzed, and a spectral clustering algorithm that automatically determines the number of clusters is proposed. Furthermore, an algorithm for constructing a discrete Morse function to find the optimal solution is proposed, proving that the constructed function is the optimal discrete Morse function. At the same time, two optimization models based on the discrete Morse theory are constructed. Finally, the optimization model based on discrete Morse theory is applied to cluster analysis, and a density clustering algorithm based on the discrete Morse optimization model is proposed. Results: This study is focused on designing and implementing a partitional-based clustering algorithm based on big data, that is suitable for clustering huge datasets to meet low computational requirements. The experiments are conducted in terms of time and space complexity and it is observed that the measure of clustering quality and the run time is capable of running in very less time without negotiating the quality of clustering. The results show that the experiments are carried out on the artificial data set and the UCI data set. Conclusion: The efficiency and superiority of the new model, are verified by comparing it with the clustering results of the DBSCAN algorithm.

The area under the ROC curve as a measure of clustering quality

The Area Under the the Receiver Operating Characteristics (ROC) Curve, referred to as AUC, is a well-known performance measure in the supervised learning domain. Due to its compelling features, it has been employed in a number of studies to evaluate and compare the performance of different classifiers. In this work, we explore AUC as a performance measure in the unsupervised learning domain, more specifically, in the context of cluster analysis. In particular, we elaborate on the use of AUC as an internal/relative measure of clustering quality, which we refer to as Area Under the Curve for Clustering (AUCC). We show that the AUCC of a given candidate clustering solution has an expected value under a null model of random clustering solutions, regardless of the size of the dataset and, more importantly, regardless of the number or the (im)balance of clusters under evaluation. In addition, we elaborate on the fact that, in the context of internal/relative clustering validation as we consider, AUCC is actually a linear transformation of the Gamma criterion from Baker and Hubert (1975), for which we also formally derive a theoretical expected value for chance clusterings. We also discuss the computational complexity of these criteria and show that, while an ordinary implementation of Gamma can be computationally prohibitive and impractical for most real applications of cluster analysis, its equivalence with AUCC actually unveils a much more efficient algorithmic procedure. Our theoretical findings are supported by experimental results. These results show that, in addition to an effective and robust quantitative evaluation provided by AUCC, visual inspection of the ROC curves themselves can be useful to further assess a candidate clustering solution from a broader, qualitative perspective as well.

Dirichlet process mixture models for single-cell RNA-seq clustering.

ABSTRACTClustering of cells based on gene expression is one of the major steps in single-cell RNA-sequencing (scRNA-seq) data analysis. One key challenge in cluster analysis is the unknown number of clusters and, for this issue, there is still no comprehensive solution. To enhance the process of defining meaningful cluster resolution, we compare Bayesian latent Dirichlet allocation (LDA) method to its non-parametric counterpart, hierarchical Dirichlet process (HDP) in the context of clustering scRNA-seq data. A potential main advantage of HDP is that it does not require the number of clusters as an input parameter from the user. While LDA has been used in single-cell data analysis, it has not been compared in detail with HDP. Here, we compare the cell clustering performance of LDA and HDP using four scRNA-seq datasets (immune cells, kidney, pancreas and decidua/placenta), with a specific focus on cluster numbers. Using both intrinsic (DB-index) and extrinsic (ARI) cluster quality measures, we show that the performance of LDA and HDP is dataset dependent. We describe a case where HDP produced a more appropriate clustering compared to the best performer from a series of LDA clusterings with different numbers of clusters. However, we also observed cases where the best performing LDA cluster numbers appropriately capture the main biological features while HDP tended to inflate the number of clusters. Overall, our study highlights the importance of carefully assessing the number of clusters when analyzing scRNA-seq data.

An Improved Similarity-Based Clustering Algorithm for Multi-Database Mining.

Clustering algorithms for multi-database mining (MDM) rely on computing pairwise similarities between n multiple databases to generate and evaluate candidate clusterings in order to select the ideal partitioning that optimizes a predefined goodness measure. However, when these pairwise similarities are distributed around the mean value, the clustering algorithm becomes indecisive when choosing what database pairs are considered eligible to be grouped together. Consequently, a trivial result is produced by putting all the n databases in one cluster or by returning n singleton clusters. To tackle the latter problem, we propose a learning algorithm to reduce the fuzziness of the similarity matrix by minimizing a weighted binary entropy loss function via gradient descent and back-propagation. As a result, the learned model will improve the certainty of the clustering algorithm by correctly identifying the optimal database clusters. Additionally, in contrast to gradient-based clustering algorithms, which are sensitive to the choice of the learning rate and require more iterations to converge, we propose a learning-rate-free algorithm to assess the candidate clusterings generated on the fly in fewer upper-bounded iterations. To achieve our goal, we use coordinate descent (CD) and back-propagation to search for the optimal clustering of the n multiple database in a way that minimizes a convex clustering quality measure in less than iterations. By using a max-heap data structure within our CD algorithm, we optimally choose the largest weight variable at each iteration i such that taking the partial derivative of with respect to allows us to attain the next steepest descent minimizing without using a learning rate. Through a series of experiments on multiple database samples, we show that our algorithm outperforms the existing clustering algorithms for MDM.

Outliers in Covid 19 data based on Rule representation - the analysis of LOF algorithm

The article concerns the detection of outliers in rule-based knowledge bases containing data on Covid 19 cases. The authors move from the automatic generation of a rule-based knowledge base from source data by clustering rules in the knowledge base to optimize inference processes and to detecting unusual rules allowing for the optimal structure of rule groups. The paper presents a two-phase procedure, wherein in the first phase, we look for the optimal structure of rule clusters when there are outlier rules in the knowledge base. In the second phase, we detect outliers in the rules using the LOF (Local Outlier Factor) algorithm. Then we eliminate the unusual rules from the database and check whether the selected cluster quality measures are responded positively to the elimination of outliers, which would indicate that the rules were rightly considered outliers. The performed experiments confirmed the effectiveness of the LOF algorithm and selected cluster quality measures in the context of detecting atypical rules. The detection of such rules can support knowledge engineers or domain experts in knowledge mining to improve the completeness of the knowledge base, which is usually the basis of the decision support system.

Ensembling of Gene Clusters Utilizing Deep Learning and Protein-Protein Interaction Information.

Cluster ensemble techniques aim to combine the outputs of multiple clustering algorithms to obtain a single consensus partitioning. The current paper reports about the development of a cluster ensemble based technique combining the concepts of multiobjective optimization and deep-learning models for gene clustering where some additional protein-protein interaction information are utilized for generating the consensus partitioning. The proposed ensemble based framework works in four phases: (i) filtering out the irrelevant genes from the microarray dataset: only the statistically significant genes are considered for further data analysis; (ii) generation of diverse base partitionings: a multi-objective optimization-based clustering technique is proposed which simultaneously optimizes three different cluster quality measures and generates a set of partitioning solutions on the Pareto optimal front; (iii) generation of a consensus partitioning: mentha scores, calculated by accessing a highly enriched protein-protein interaction archive named mentha, of different clustering solutions are considered for generating a weighted incidence matrix; (iv) finally, two approaches are used to generate a consensus partitioning from the obtained incidence matrix. The first approach is based on a traditional machine learning method, and another approach exploits the graph partitioning algorithm and two deep neural models to generate the final clustering. To validate the efficacy of the proposed ensemble framework, it is applied on five gene expression datasets. We present a comparative analysis of the proposed technique over different clustering algorithms in terms of biological homogeneity index (BHI) and biological stability index (BSI). The traditional approach attains an average 3 and 2 percent improvements over the best non-dominated solution with respect to BHI and BSI, respectively, whereas deep learning models illustrate an average 6.8 and 1.5 percent improvements over the proposed traditional approach with respect to BHI and BSI, respectively. Subsequently, Welch's t-test is executed to prove that the results obtained by the proposed methods are statistically significant. Availability of data and materials: https://github.com/sduttap16/DeepEnsm.

A polynomial algorithm for balanced clustering via graph partitioning

The objective of clustering is to discover natural groups in datasets and to identify geometrical structures which might reside there, without assuming any prior knowledge on the characteristics of the data. The problem can be seen as detecting the inherent separations between groups of a given point set in a metric space governed by a similarity function. The pairwise similarities between all data objects form a weighted graph whose adjacency matrix contains all necessary information for the clustering process. Consequently, the clustering task can be formulated as a graph partitioning problem. In this context, we propose a new cluster quality measure which uses the ratio of intra- and inter-cluster variance and allows us to compute the optimal clustering under the min-max principle in polynomial time. Our algorithm can be applied to both partitional and hierarchical clustering.

A comparative user study of visualization techniques for cluster analysis of multidimensional data sets

This article presents an empirical user study that compares eight multidimensional projection techniques for supporting the estimation of the number of clusters, [Formula: see text], embedded in six multidimensional data sets. The selection of the techniques was based on their intended design, or use, for visually encoding data structures, that is, neighborhood relations between data points or groups of data points in a data set. Concretely, we study: the difference between the estimates of [Formula: see text] as given by participants when using different multidimensional projections; the accuracy of user estimations with respect to the number of labels in the data sets; the perceived usability of each multidimensional projection; whether user estimates disagree with [Formula: see text] values given by a set of cluster quality measures; and whether there is a difference between experienced and novice users in terms of estimates and perceived usability. The results show that: dendrograms (from Ward’s hierarchical clustering) are likely to lead to estimates of [Formula: see text] that are different from those given with other multidimensional projections, while Star Coordinates and Radial Visualizations are likely to lead to similar estimates; t-Stochastic Neighbor Embedding is likely to lead to estimates which are closer to the number of labels in a data set; cluster quality measures are likely to produce estimates which are different from those given by users using Ward and t-Stochastic Neighbor Embedding; U-Matrices and reachability plots will likely have a low perceived usability; and there is no statistically significant difference between the answers of experienced and novice users. Moreover, as data dimensionality increases, cluster quality measures are likely to produce estimates which are different from those perceived by users using any of the assessed multidimensional projections. It is also apparent that the inherent complexity of a data set, as well as the capability of each visual technique to disclose such complexity, has an influence on the perceived usability.

A density-based statistical analysis of graph clustering algorithm performance

Abstract We introduce graph clustering quality measures based on comparisons of global, intra- and inter-cluster densities, an accompanying statistical significance test and a step-by-step routine for clustering quality assessment. Our work is centred on the idea that well-clustered graphs will display a mean intra-cluster density that is higher than global density and mean inter-cluster density. We do not rely on any generative model for the null model graph. Our measures are shown to meet the axioms of a good clustering quality function. They have an intuitive graph-theoretic interpretation, a formal statistical interpretation and can be tested for significance. Empirical tests also show they are more responsive to graph structure, less likely to breakdown during numerical implementation and less sensitive to uncertainty in connectivity than the commonly used measures.

DATA STORING AND RETRIEVAL METHOD IN BIG DATA USING FUZZY BASED SCALABLE CLUSTERING ALGORITHMS

A massive volume of digital data holding valuable information, called Big Data, is produced each generation. To process and excavate such valuable information, clustering is commonly used as a data investigation technique. A huge amount of Big Data diagnostics contexts have been established to measure the clustering procedures used for big data analysis. There exists one and only framework called Fuzzy based mechanism which actually fits in for iterative method by associate in storage divisions and accessible. The proposed algorithm is motivated towards the design and implementation of fuzzy based clustering algorithms on big data, which could be present for clustering huge datasets due to their low computational necessities. In this paper, we propose Random Data Storing with Optimization Fuzzy Logic algorithm (RDS-FLA) applied on cluster data to handle the tasks that are connected with big data clustering. Experimental trainings data taking place several big datasets have been showed. The performance of RDS-FLA is tried in evaluation with the proposed scalable form of the temporal fuzzy and Random data storing that is implemented on the big data cluster. The computation outcomes are recounted in terms of time and space complexity, run time and measure of clustering quality, showing that RDS-FLA is able to run in much less time without compromising the clustering quality. Thus, the algorithm proposed alleviates the processing time and increases the security of storage data effectively. Advantages such as cost optimization and efficiency in data security can be identified from the experimental results of proposed algorithm.

An ensemble based on a bi-objective evolutionary spectral algorithm for graph clustering

Graph clustering is a challenging pattern recognition problem whose goal is to identify vertex partitions with high intra-group connectivity. This paper investigates a bi-objective problem that maximizes the number of intra-cluster edges of a graph and minimizes the expected number of inter-cluster edges in a random graph with the same degree sequence as the original one. The difference between the two investigated objectives is the definition of the well-known measure of graph clustering quality: the modularity. We introduce a spectral decomposition hybridized with an evolutionary heuristic, called MOSpecG, to approach this bi-objective problem and an ensemble strategy to consolidate the solutions found by MOSpecG into a final robust partition. The results of computational experiments with real and artificial LFR networks demonstrated a significant improvement in the results and performance of the introduced method in regard to another bi-objective algorithm found in the literature. The crossover operator based on the geometric interpretation of the modularity maximization problem to match the communities of a pair of individuals was of utmost importance for the good performance of MOSpecG. Hybridizing spectral graph theory and intelligent systems allowed us to define significantly high-quality community structures.

Spectral Clustering in Heterogeneous Information Networks

A heterogeneous information network (HIN) is one whose objects are of different types and links between objects could model different object relations. We study how spectral clustering can be effectively applied to HINs. In particular, we focus on how meta-path relations are used to construct an effective similarity matrix based on which spectral clustering is done. We formulate the similarity matrix construction as an optimization problem and propose the SClump algorithm for solving the problem. We conduct extensive experiments comparing SClump with other state-of-the-art clustering algorithms on HINs. Our results show that SClump outperforms the competitors over a range of datasets w.r.t. different clustering quality measures.

Fusion of evolvable genome structure and multi-objective optimization for subspace clustering

Subspace clustering techniques become paramount in pattern recognition for detecting local variations from high dimensional data. Several techniques exist in the recent literature for subspace clustering, majority of which optimize implicitly or explicitly a single cluster quality measure. Inspired by the success of multi-objective optimization in solving clustering problem, we developed a multi-objective based subspace clustering technique in this paper. The proposed technique simultaneously optimizes two subspace cluster quality measures, capable of capturing different cluster shapes/properties. Two existing cluster quality measures, XB-index and PBM-index, are modified to develop subspace cluster validity indices, and then those are used as optimization criteria. These cluster validity indices measure the appropriateness of generated subspace clusters in terms of intra-subspace cluster similarity and separation between subspace clusters. The proposed approach utilizes a new evolvable genome structure which stores the information about subspaces in its phenotype and genotype and evolves this genome structure with the help of different genetic operators. The developed algorithm is applied on ten standard real-life data sets and sixteen synthetic datasets for identifying different subspace clusters. The results obtained by this algorithm are compared against some state-of-the-art techniques with respect to different performance metrics. Experimentation reveals that the proposed algorithm is able to take advantages of its evolvable genomic structure and multi-objective based framework and it can be applied to any data set. In a part of the paper, the efficacy of the proposed technique is also shown for bi-clustering of gene-expression data sets.

An efficient hybrid PSO polygamous crossover based clustering algorithm

Clustering of data into cohesive groups is an open area of research with lots of applications in different domains. Many traditional and metaheuristic algorithms have been proposed in the literature, but the main inherent problem with most of these algorithms is that they can easily get trapped in local optima and can lead to premature convergence. Thus a significant balance is required between exploration and exploitation to find a near optimal solution. This paper attempts to resolve this problem by proposing a real encoded hybrid algorithm (PSOPC) using PSO for global search and polygamous approach for crossover in order to refine the exploration and exploitation strategy. Parameters like inertia weight, crossover probability and alpha values in arithmetic crossover are also tuned dynamically to refine the optimization process. The Proposed hybrid algorithm is simulated on seven real life data sets. It has also been compared with other four standard well known metaheuristic clustering algorithms i.e. Particle Swarm Optimization, Genetic Algorithm, Differential Evolution, Firefly Algorithm and Grey Wolf Optimization. The computational results demonstrate that the PSOPC outperforms other approaches in context of within cluster distance, cluster quality measures and convergence speed to find the near optimal solutions. Simulation results clearly reveal that the proposed algorithm PSOPC is able to generate compact clusters. Various external quality evaluation measurements (like Precision, Sensitivity, Accuracy and G-measure) used for quality evaluation demonstrated that the proposed algorithm is able to perform better clustering than the other compared algorithms.

Coherent network partitions

Graph clustering is widely applied in the analysis of cellular networks reconstructed from large-scale data or obtained from experimental evidence. Here we introduce a new type of graph clustering based on the concept of coherent partition. A coherent partition of a graph G is a partition of the vertices of G that yields only disconnected subgraphs in the complement of G. The coherence number of G is then the size of the smallest edge cut inducing a coherent partition. A coherent partition of G is optimal if the size of the inducing edge cut is the coherence number of G. Given a graph G, we study coherent partitions and the coherence number in connection to (bi)clique partitions and the (bi)clique cover number. We show that the problem of finding the coherence number is NP-hard, but is of polynomial time complexity for trees. We also discuss the relation between coherent partitions and prominent graph clustering quality measures.

Solving a Potential Clustering Game

Data clustering is the unsupervised classification of a set of objects into groups (clusters), according to their similarities. This can be seen as a form of equilibrium, which is the motivation that led to recent formulations of the data clustering task using game theoretic models. In this context, we propose a novel game-theoretic clustering approach reducing the clustering task to that of searching for a pure Nash equilibrium of a potential game, which corresponds to a stable clustering. Interestingly, the existence and the convergence towards such equilibrium are established, and we experimentally prove that such stability is not always guaranteed by the classical k-means algorithm. We also propose an iterative best-response algorithm for solving this potential clustering game. This algorithm is implemented and tested on several real-world and artificial datasets. Considering most of clustering quality measures, the obtained results are compared to those provided by both the classical k-means and by an hybridization of these two algorithms.